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Ever since Newton published his universal law of gravitation in 1687, anyone with a slide rule and a half decent education could calculate the force of gravity on a falling body or a planet in orbit.

Newton saw gravity as an attractive force between all bits of matter. So every speck of matter in the universe is literally attracting every other speck of matter to it. The heavier a thing is, the more attractive it is, and the force always gets stronger up close.

So you and planet Earth pull on each other equally, but because it's such a heavy lump of a planet, you're stuck to the Earth while even your most Newtonian attraction doesn't make it budge noticeably. But if a decent sized planet swung our way you'd soon see Earth moving towards the thing. So fickle.

Newton's gravity was beautifully simple, and his law had worked spectacularly well for calculating gravitational force for a couple of centuries. Obviously something had to be done!

Einstein tackled gravity from a completely different angle. Already on a roll with special relativity, where he showed that mass and energy were really two versions of the same thing (read more about E=mc2), he couldn't get the idea that gravity wasn't any different from uniform acceleration out of his head.

Relativity, gravity and space elevators

Einstein's thinking went like this. If you're in a stationary elevator and you drop a ball (theoretical physicists never travel without one), the ball will fall to the floor of the lift at 9.8 metres per second per second — that's the rate of gravitational acceleration for everything that falls to Earth.

Now if some nefarious fiend cut the cables on your elevator, you and the ball would go into freefall. For a few seconds you'd both float in the elevator, because it's falling away beneath you just as fast as you're falling towards Earth. You'd experience the majesty of weightlessness, right up until your thigh bones rammed through your shoulders. But focus on the weightlessness people!

Meanwhile someone else is in another elevator way out in space that's accelerating upwards at 9.8 metres per second per second (clearly for all his genius the man couldn't imagine a rocket, let alone a Tardis). When they drop their compulsory travel ball, it will fall to the floor of their speeding elevator exactly the same way yours did — even though there's no gravity in sight. And if their space elevator came to a halt, your mate and their ball would go into weightlessness that looks and feels exactly like your freefall, minus the imminent skeletal realignment.

Most of us would just leave an idea like that right where we found it, maybe dragging it out for the odd philosophical dinner party. But Einstein wasn't one for leaving well enough alone. The idea that there's no difference between the effect of gravity and the effect of uniform acceleration became known as the equivalence principle. And together with the idea of spacetime, it's the basis of Einstein's take on gravity — his theory of general relativity.

Spacetime is where (and when) it's at, man

In Newton's world it's a gravitational force that causes bits of matter to accelerate towards each another. Einstein put the acceleration down to the fact that matter warps spacetime.

Spacetime isn't an actual thing, it's the geometry that the universe works in.

We're all used to space and to time — events always involve a where and a when. So the idea of four dimensions (the up/down, left/right and front/back of space, plus time) seems pretty straightforward.

But spacetime is more than just a bundling of coordinates. Space and time are part of the same deal: they mix and match and morph into one another. If you change space, you affect time. And the one thing that's guaranteed to mess with spacetime is matter.

Every bit of matter in the universe is distorting the bit of spacetime it exists in. And distortions in spacetime affect the way matter and energy (like light) move through space and time.

It's the mass of matter that's the real spacetime bender, so the heavier matter is, the more it distorts (or warps, curves or bends) spacetime. And thanks to E=mc2, the more energy a thing has, the more mass, so energy distorts spacetime too.

Planets make big dents in spacetime, and massive things like stars cause enormous wells — like the one in the two-dimensional diagram at the start of the story. It's hard to find a graphics program that renders four-dimensional spacetime accurately, but for our 2D-loving brains, this image shows how curved spacetime draws things towards massive objects. The rocket passing the star, and all who sail in her, will feel a strong pull towards it. That tug isn't a force, it's the acceleration you get when you scoot along a curved bit of spacetime. It's gravity. (Get your Play School craft gear and follow these instructions for a hands-on version of curved spacetime).

Curvy spacetime is a pretty out there explanation for gravity, and in science the wackier the idea, the more hard core the maths you need to back it up. Einstein had the heavy duty equations to explain his theory for anyone who could follow them. And in most situations his calculations gave the same results as Newton's much simpler law. But Einstein's gravity did much more.

Relativistic gravity applied beautifully when things got very fast (near light speed), or very massive (star size), where Newton's law was a dud. And it accounted for why light bends near massive objects (it does pretty much the same thing the alien tennis ball does in the diagram above). Newtonian gravity only applied to objects with mass — matter, not energy like light.

More impressive still, general relativity predicted the effect that gravity has on the time part of spacetime: time literally slows down in curvy spacetime. The curvier the spacetime, the stronger the gravity, the slower the time. It's called gravitational time dilation, and along with the other predictions it's been well and truly checked off the 'things to prove' list. In 2010 a couple of ridiculously accurate atomic clocks were set at slightly different heights, with one 33 centimetres higher than the other. The difference in the curvature of spacetime due to the Earth's mass was noticeable even over that ridiculously small distance — the higher clock will gain the equivalent of 90 billionths of a second over the next 80 years.

And there's another relativistic gravitational time dilation experiment that you conduct every time you use a GPS.

GPS relies on satellites orbiting high above us, where Earth's gravity is weaker (spacetime is less warped by Earth's mass the further away you go). So the ultra-precise atomic clocks in the satellites run 45 millionths of a second faster per day than clocks here on the ground, deep in the Earth's gravitational well. If those millionths of a second weren't taken into account when the satellite signals were synced, your GPS coordinates would be out by more than 10 kilometres. Between that and the annoying voices GPS would never have taken off.

Einstein's take on gravity has been incredibly successful from our dashboards to our space programs. It's gone where no Newtonian equation could go. And it might have been the end of the "what exactly is gravity?" question if it wasn't for one thing — it doesn't work or play well with the physics at the other end of the scale: the laws of quantum mechanics.

The two theories can't both be right. And no doubt Einstein would be happy to know that thousands of research physicists have been tackling the mismatch for almost a century, and the hunt for a single explanation of the massive and the tiny is still on. More on that next time.

Thanks to Prof David Jamieson from the School of Physics at The University of Melbourne.